Advertisements
Advertisements
प्रश्न
Find the next 4 terms of the sequence `1/6, 1/4, 1/3`. Also find Sn.
Advertisements
उत्तर
The given sequence is `1/6, 1/4, 1/3`
The above sequence is an A.P.
∴ a = `1/6`
d = `1/4 -1/6`
= `(3 - 2)/12`
= `1/12`
The next four terms of the sequence are
t4 = t3 + d
= `1/3 + 1/12`
= `5/12`
t5 = t4 + d
= `5/12 + 1/12`
= `6/12`
= `1/2`
t6 = t5 + d
= `1/2 + 1/12`
= `7/12`
t7 = t6 + d
= `7/12 + 1/12`
= `8/12`
= `2/3`
`S_n = n/2 [2a + (n - 1)d]`
= `n/2 [2(1/6) + (n - 1)(1/12)]`
= `n/2 (1/3 + 1/12 n - 1/12)`
= `n/2(n/12 + 1/4)`
∴ `S_n = (n(n + 3))/24`
APPEARS IN
संबंधित प्रश्न
An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term of the A.P.
If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?
Determine the A.P. whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant will be the same as the class, in which they are studying, e.g., a section of class I will plant 1 tree, a section of class II will plant 2 trees, and so on till class XII. There are three sections of each class. How many trees will be planted by the students?
If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
Show that (a – b)2, (a2 + b2) and (a2 + b2) are in AP.
Find the first term and common difference for the A.P.
127, 135, 143, 151,...
In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.
The common difference of an A.P., the sum of whose n terms is Sn, is
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
In a ‘Mahila Bachat Gat’, Sharvari invested ₹ 2 on first day, ₹ 4 on second day and ₹ 6 on third day. If she saves like this, then what would be her total savings in the month of February 2010?
Find t21, if S41 = 4510 in an A.P.
An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.
Solve the equation
– 4 + (–1) + 2 + ... + x = 437
If the first term of an A.P. is 5, the last term is 15 and the sum of first n terms is 30, then find the value of n.
